The Professional Education and Development of Teachers of Mathematics New ICMI Study Series VOLUME 11 Published under the auspices of the International Commission on Mathematical Instruction under the general editorship of Mich` le Artigue, President e Bernard R Hodgson, Secretary-General The titles published in this series are listed at the end of this volume Ruhama Even · Deborah Loewenberg Ball Editors The Professional Education and Development of Teachers of Mathematics The 15th ICMI Study 123 Editors Ruhama Even Weizmann Institute of Science Rehovot, Israel ruhama.even@weizmann.ac.il ISBN: 978-0-387-09600-1 DOI 10.1007/978-0-387-09601-8 Deborah Loewenberg Ball University of Michigan Ann Arbor, MI, USA dball@umich.edu e-ISBN: 978-0-387-09601-8 Library of Congress Control Number: 2008930564 c Springer Science+Business Media, LLC 2009 All rights reserved This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013, USA), except for brief excerpts in connection with reviews or scholarly analysis Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights Printed on acid-free paper springer.com Contents Setting the Stage for the ICMI Study on the Professional Education and Development of Teachers of Mathematics Ruhama Even and Deborah Loewenberg Ball Section Initial Mathematics Teacher Education 11 Editor: Stephen Lerman Theme 1.1 The Preparation of Teachers 13 Editor: Jarmila Novotn´ a 1.1.1 Overview of Teacher Education Systems Across the World 15 Maria Teresa Tatto, Stephen Lerman, and Jarmila Novotn´ a 1.1.2 Components of Mathematics Teacher Training 25 Peter Liljedahl, and V Durand-Guerrier, C Winsløw, I Bloch, P Huckstep, T Rowland, A Thwaites, B Grevholm, C Bergsten, J Adler, Z Davis, M Garcia, V S´ nchez, J Proulx, J Flowers, a R Rubenstein, T Grant, K Kline, P Moreira, M David, C Opolot-Okurut, O Chapman 1.1.3 Practising Mathematics Teacher Education: Expanding The Realm of Possibilities 35 Uwe Gellert, and S Amato, M Bairral, L Zanette, I Bloch, G Gadanidis, I Namukasa, G Krummheuer, B Grevholm, C Bergsten, D Miller, A Peter-Koop, B Wollring, J Proulx, L M Rosu, B Arvold, N Sayac 1.1.4 Learning to Teach Mathematics: Expanding the Role of Practicum as an Integrated Part of a Teacher Education Programme 57 v vi Contents Christer Bergsten, Barbro Grevholm, Franco Favilli, and N Bednarz, J Proulx, D Mewborn, P Johnson, T Rowland, A Thwaites, P Huckstep, L DeBlois, J.-F Maheux, O Chapman, L M Rosu, B Arvold, U Gellert, G Krummheuer, J Skott, K G Garegae, P A Chakalisa, D Kadijevich, L Haapasalo, J Hvorecky, A Carneiro Abrah˜ o, A T de Carvalho a Correa de Oliveira, J Novotn´ , M Hofmannov´ , a a D Tirosh, P Tsamir Theme 1.2 Student Teachers’ Experiences and Early Years of Teaching 71 Editor: Stephen Lerman 1.2.1 Studying Student Teachers’ Voices and Their Beliefs and Attitudes 73 Stephen Lerman, and S A Amato, N Bednarz, M M M S David, V Durand-Guerrier, G Gadanis, P Huckstep, P C Moreira, F Morselli, N MovshovitzHadar, I Namukasa, J Proulx, T Rowland, A Thwaites, C.Winsløw 1.2.2 School Experience During Pre-Service Teacher Education from the Students’ Perspective 83 Merrilyn Goos, and B Arvold, N Bednarz, L DeBlois, J Maheux, F Morselli, J Proulx 1.2.3 First Years of Teaching 93 Carl Winsløw, and C Bergsten, D Butlen, M David, P G´ mez, M Goos, B Grevholm, S Li, P Moreira, o N Robinson, N Sayac, J Schwille, T Tatto, A White, T Wood Theme 1.3 Mathematics Educators’ Activities and Knowledge 103 Editor: Pedro G´ mez o 1.3.1 Mathematics Educators’ Knowledge and Development 105 Orit Zaslavsky 1.3.2 Becoming a Teacher Educator: Perspectives from the United Kingdom and the United States 113 Sue Pope and Denise S Mewborn 1.3.3 Educators Reflecting on (Researching) Their Own Practice121 Olive Chapman Contents vii 1.3.4 Educators and the Teacher Training Context 127 Richard Millman, Paola Iannone and Peter Johnston-Wilder Initial Mathematics Teacher Education: Comments and Reflections 135 Gilah Leder Initial Mathematics Teacher Education: Comments and Reflections 139 Shiqi Li Section Learning in and from Practice 143 Editor: Barbara Jaworski Theme 2.1 Development of Teaching in and from Practice 149 Brent Davis, Laurinda Brown, and T Cedillo, C.-M Chiocca, S Dawson, J Gim´ nez, J Hodgen, B Jaworski, M Kidd, e D Siemon Editor: Barbara Jaworski Theme 2.2 Mathematics Teachers’ Professional Development: Processes of Learning in and from Practice 167 Jo˜ o Filipe Matos, Arthur Powell, Paola Sztajn, and L Ejersbø, a J Hovermill Editor: Jo˜ o Filipe Matos a Theme 2.3 Tools and Settings Supporting Mathematics Teachers’ Learning in and from Practice 185 Jo˜ o Pedro da Ponte, Orit Zaslavsky, Ed Silver, Marcelo de a Carvalho Borba, Marja van den, Heuvel-Panhuizen, Hagar Gal, Dario Fiorentini, Rosana Miskulin, C´ rmen Passos, Gilda de La a Rocque Palis, Rongjin Huang, Olive Chapman Editor: Marja van den Heuvel-Panhuizen Theme 2.4 The Balance of Teacher Knowledge: Mathematics and Pedagogy 211 Michael Neubrand, Nanette Seago, and C Agudelo-Valderrama, L DeBlois, R Leikin Editor: Terry Wood Learning in and from Practice: Comments and Reflections 227 Aline Robert Established Boundaries? A Personal Response to Learning in and from Practice 231 Chris Breen viii Contents Section Key Issues for Research in the Education and Professional Development of Teachers of Mathematics 237 3.1 Some Reflections on Education, Mathematics, and Mathematics Education 239 Ubiratan D’Ambrosio 3.2 Toward a More Complete Understanding of PracticeBased Professional Development for Mathematics Teachers 245 Edward A Silver 3.3 Public Writing in the Field of Mathematics Teacher Education 249 Jill Adler and Barbara Jaworski Strengthening Practice in and Research on the Professional Education and Development of Teachers of Mathematics: Next Steps 255 Deborah Loewenberg Ball and Ruhama Even ICMI Study-15: List of Participants 261 Author Index 265 Subject Index 271 Lead Contributors Jill Adler University of the Witwatersrand, Johannesburg, South Africa Deborah Loewenberg Ball University of Michigan, Ann Arbor, MI, USA Christer Bergsten Linkă ping University, Sweden o Chris Breen University of Cape Town, South Africa Laurinda Brown University of Bristol, Bristol, UK Olive Chapman University of Calgary, Canada Ubiratan D’Ambrosio Universidade Estadual de Campinas, Campinas, SP, BR Brent Davis University of British Columbia, British Columbia, Canada Ruhama Even Weizmann Institute of Science, Israel Franco Favilli University of Pisa, Italy Uwe Gellert Freie Universită t Berlin, Germany a Merrilyn Goos University of Queensland, Australia Pedro G´ mez o Universidad de Granada, Spain ix ICMI Study-15: List of Participants Local Organising Committee da Silva, Heloisa Francisco, Carlos Alberto Healy, Lulu Lins, Romulo Ol´mpio Jr., Antonio ı Oliveira, Roney Pacheco, Ed´lson ı Penteado, Miriam Teixeira, Marcos Study assistants Ayalon, Michal, ISRAEL Ridenout, Terri, USA Editorial Board Chris Breen Fr´ d´ ric Gourdeau e e Barbara Jaworski Gilah Leder Stephen Lerman Shiqi Li Romulo Lins Jo˜ o Filipe de Lacerda Matos a Jarmila Novotna Aline Robert Marja van den Heuvel-Panhuizen Terry Wood International Programme Committee Deborah Loewenberg Ball (Co-Chair IPC) University of Michigan USA Ruhama Even (Co-Chair IPC) Weizmann Institute of Science ISRAEL The members of the International Programme Committee (IPC) are: Jo Boaler Stanford University USA Chris Breen University of Cape Town SOUTH AFRICA 263 264 ICMI Study-15: List of Participants Fr´ d´ ric Gourdeau e e Universit´ Laval e CANADA Marja van den Heuvel-Panhuizen Utrecht University NETHERLANDS Barbara Jaworski Loughborough University UK Gilah Leder La Trobe University AUSTRALIA Shiqi Li East China Normal University CHINA Romulo Lins (Chair of the Local Organising Committee) State University of Sao Paulo at Rio Claro BRAZIL Jo˜ o Filipe Matos a Universidade Lisboa PORTUGAL Jarmila Novotna Charles University CZECH REPUBLIC Aline Robert IUFM de Versailles FRANCE Ex-officio members: Bernard R Hodgson Secretary-General of ICMI Universit´ Laval e CANADA Hyman Bass President of ICMI University of Michigan USA Author Index A Adler, A., 78 Adler, J., 25, 26, 42, 78, 108, 175, 180, 249, 253 Agudelo-Valderrama, C., 211, 213, 215, 216 Alrø, H., 42 Amato, S., 35, 37, 79 Amato, S A., 79 Amit, M., 189 Ammons, A R., 236 Arbaugh, F., 108 Arnot, M., 73 Arvold, B., 35, 52, 53, 57, 64, 83, 87 Askew, M., 131 Atkinson, T., 217 B Bairral, M., 35, 45, 66, 202, 203 Ball, D., 27, 30, 57, 95, 108, 175, 177, 212, 213, 220, 246, Ball, D L., 1, 27, 30, 57, 95, 108, 175, 177, 168, 169, 178, 191, 193, 212, 213, 245, 246, 255 Bao, J., 193 Barb´ , J., 94, 96 e Barton, L., 114 Bass, H., 95, 177, 191, 212, 213, 220, 246 Bateson, G., 156 Bauersfeld, H., 42 Baumert, J., 214 Becker, J R., 123, 124 Bednarz, N., 57, 58, 60, 73, 79, 83, 84, 87, 90 Ben-Chaim, D., 123 Berenson, S B., 177 Bergsten, C., 25, 35, 42, 44, 45, 57, 58, 59, 60, 93, 94, 96 Bergsten, Ch., 25, 42, 44, 45, 59, 60, 94, 96 Bernstein, B., 42 Bishop, A., 213 Blanton, M L., 123, 124 Bloch, I., 25, 35, 37, 39, 40 Blum, W., 214 Boero, P., Borasi, R., 169 Borba, M C., 202, 203, 204, 205 Bosch, M., 94 Bowers, J., 123, 124 Branca, N., 219, 220 Breen, C., 86, 231 Britton, E., 93, 98 Brousseau, G., 25, 84, 218 Brown, A., 74 Brown, C A., 189, 108, 152, 154, 156, 159, 189 Brown, C., 59 Brown, J S., 84 Brown, L., 149, 154 Brown, M., 42, 131 Brown, T., 42, 63, 73, 108, 131, 152, 154, 156, 159, 189 Bruner, J, 26 Brunner, M., 213, 214 Bull, B., 216 Burton, L., 130 Butlen, D., 93, 96 C Campbell S R., 30 Carneiro Abrah˜ o, A M., 57, 66 a Catherine-Marie Chiocca, 149 Cavey, L O., 177 Cecilia Agudelo-Valderrama, 211 Chakalisa, P A., 57, 66 Chan, C., 123, 124 Chapman, O., 25, 27, 29, 57, 64, 108, 121, 123, 124, 185, 187, 196, 199 Charlot, B., 86 Chernoff, E., 26 265 266 Chevallard, Y., 94, 96 Clarke, B., 213, 215 Clarke, D., 74 Claxton, G., 217 Cobb, P., 42, 146 Cochran-Smith, M., 169 Cohen, D K., 168, 169, 178, 191, 193, 245, 246 Cohen, D., 168, 169, 178, 191, 193, 245, 246 Coles, A., 154 Collins, A., 84 Collopy, R., 219 Comiti, C., 57 Confrey, J., 146 Cooney, T J., 106, 187, 213 Cooney, T., 59, 83 Cuoco, A., 130 D D’Ambrosio, U., 239 da Ponte, J P., 46, 185, 201 David, M., 25, 28, 75, 93, 94, 95 David, M M M S., 28, 73, 75, 94, 95 Davis, B., 26, 86, 78, 149, 152, 153, 158, 253 Davis, Z., 25, 26, 78, 152, 153, 158, 253 Dawson, A J., 155, 161, 203 Dawson, S., 149 de Carvalho Correa de Oliveira, A T., 57, 66 De Corte, E., 13, 27 DeBlois, L., 57, 63, 64, 83, 90, 211, 216, 217, 218 Desgagn´ , S., 217 e Dewey, J., 26, 105, 121 Dinur, S., 213, 214 diSessa, A., 146 Doerr, H M., 123, 124, 189 Dowling, P., 74 Driscoll, M., 220 Duguid, P., 84 Durand-Guerrier, V., 25, 73, 75 E Egan, K., 26 Ejersbo, L., 179 English, L D., 189 Ensor, P., 80, 83, 90 Erikson, G., 217 Ernest, P., 27 Espinoza, L., 94 Even, R., 1, 59, 105, 255 F Fauvel, J., 212 Favilli, F., 57, 67 Author Index Feiman-Nemser, S., 62 Fennema, E., 146, 178 Fernandez, C., 177 Ferrini-Mundy, J., 213 Feuer, M J., 164 Fey, J T., 168 Findell, B., 186, 212 Fiorentini, D., 185, 198 Flowers, J., 25, 28, 30 Fonzi, J., 169 Forman, E., 42 Francisco, J M., 177, 211 Freundenthal, H., 167 Fried, M N., 189 Furlong, J., 114 G G´ mez, P., 93, 99, 103 o Gadanidis, G., 35, 37, 38 Gadanis, G., 73, 74, 75, 76 Gal, H., 150, 185, 191, 192, 193, 194, 195 Gale, J., 150 Garc´a, M., 25, 26 ı Garegae, K G., 57, 66 Gasc´ n, J., 94 o Gates, P., 216 Gellert, U., 35, 48, 50, 51, 52, 57, 65 Gim´ nez, J., 149, 202, 203 e Goldenberg, E P., 130 Goldsmith, L T., 216, 220 Goodchild, S., 59 Goos, M., 62, 83, 88, 89, 93 Grant, T., 25, 28 Gravemeijer, K., 146 Green, T., 27 Grevholm, B., 25, 35, 42, 44, 45, 57, 58, 59, 60, 93, 94, 96 Gromov, M 243 Gurevich, I., 213 H Haapasalo, L., 57, 66 Haggarty, L., 117 Hanley, U., 63 Hanna, E., 177, 179 Hanna, G., 212 Hazzan, O., 179 Heaton, R M., 123, 124 Heck, D J., 219 Henningsen, M A., 246 Henningsen, M., 186 Hershkovitz, S., 108 Hewson, P W., 168 Author Index Hiebert, J., 99, 147, 176, 177, 178, 186, 187, 258 Hill, H C., 177, 212, 219 Hill, H., 178, 213, 219 Hofmannov´ , M., 57, 67 a Huang, R., 185, 193 Huckstep, P., 25, 57, 63, 73, 78, 79, 80, 128 Hvorecky, J., 57, 66 I Iannone, P., 127 Ilany, B -S., 123 J Jahnke, H., 212 Jaworski, B., 48, 97, 106, 143, 146, 149, 151, 153, 155, 186, 187, 197, 202, 249, 254 Johnsen Høines, M., 57, 62 Johnson, D., 131 Johnson, P., 57, 58, 62 Johnston-Wilder, P., 127 Jones, D., 59 Jones, K., 117 Jones, L., 63 K Kadijevich, D., 57, 66 Kanes, C., 80 Keret, Y., 123 Kieran, C., 42 Kilpatrick, J., 2, 186, 212 Kinach, B., 123 King, E., 177 Kirsch, A., 214 Kline, K., 25, 28 Krainer, K., 108, 175, 186, 187, 202 Krauss, S., 213, 214 Krummheuer, G., 35, 51, 52, 57, 65 Kunter, M., 214 L Lacey, C., 83 Lakoff, G., 160 Lampert, M., 246 Lanier, J E., 58 Lave, J., 26, 85, 171, 174, 182 Lavie, O., 189, 190 Leatham, K., 27 Leder, G C., 135 Lehrer, R., 146 Leikin, R., 213, 214, 216, 217 Lerman, S., 11, 15, 29, 59, 62, 71, 73, 105, 150, 151, 197 Leron, U., 179 267 Levav-Waynberg, A., 213 Lewis, C., 176, 179 Li, S., 93, 95, 98, 139 Liljedahl, P., 25, 26, 29 Lin, F.-L., 108, 175 Lin, P.-J., 189 Linchevski, L., 191, 192, 193, 194 Little, J W., 58, 168, 169, 191 Llinares, S., 202 Lloyd, G., 216 Lode, B., 57, 62 Long, C., 129 Lortie, D., 27, 83 Lortie, D C., 27, 83 Loucks-Horsley, S., 168, 178 Love, N., 168 Lytle, S., 169 M Ma, L., 95, 98, 178, 213, 220 Maher, C A., 177 Maheux, J., 63, 64, 83, 90, 218 Maheux, J.-F 57, 63, 64, 83, 90, 218 Malheiros, A P S., 205 Margaret Kidd, L., 149 Mark, J., 130 Marton, F., 146 Masingila, J O., 189 Mason, J., 108, 125, 127, 130, 213 Maturana H., 218 McCallum, W., 127, 128 McCrory, R., 127, 128 McDermott, R., 174 McDiarmid, G., 27 McEwan, H., 216 McGraw, R., 205 McLaughlin, M W., 191 McNamara, O., 63, 73, 80 McTighe, J., 178 Mednikov, L., 213 Melnick, S., 27 Menter, I., 114 Mewborn, D., 57, 58, 62, 113 Mickelson,W T., 123, 124 Miles, S., 114 Miller, D., 35, 46, 47, 66 Millman, R., 127 Miskulin, R., 185 Moreira, P C., 28, 73, 75, 94, 95 Moreira, P., 25, 28, 75, 93, 94, 95 Morselli, F., 73, 75, 83, 86 Mousley, J., 48, 186, 187, 213 Movshovitz-Hadar, N., 73, 80 268 Mumme, J., 219, 220 Murata, A., 177 N Namukasa, I., 35, 37, 38, 73, 74, 75, 76 Neubrand, J., 215 Neubrand M., 211, 214 Nilssen, V., 62 Novotn´ , J., 13, 15, 57, 67, 108, 175 a O Oliveira, H., 46 Op ’T Eynde, P., 27 Opolot-Okurut, C., 25, 28, Owen, H., 233 P Paine, L., 93 Palis, G L R., 185, 189, 190 Parker, D., 253 Parker, M., 27 Passos, C L B., 185 Peled, I., 105, 106, 107, 108, 139 Pence, B J., 123, 124 Penteado, M G., 202 Peretz, D., 37 Peter-Koop, A., 35, 42, 43, 44, 129 Phillips, D C., 164 Piaget, J., 26, 218 Pimm, D., 42, 86, 93 Polanyi, M., 159 Polya, G., 129 Ponte, J P., 196, 201, 202, 205 Pope, S., 113, 117 Powell, A B., 167, 177, 236 Proulx, J., 25, 26, 35, 36, 57, 58, 60, 61, 73, 76, 78, 79, 83, 84, 86, 87, 90 R Raeithel, A., 48 Raizen, S., 93 Ralston, A., 127 Reay, D., 73 Ren´ de Cotret, S., 218 e Reys, R., 113 Rhodes, V., 131, 236 Robinson, N., 93, 236 Roddick, C., 123, 124 Romberg, T., 178 Rosu, L M., 35, 52, 53, 57, 64 Rowland, T., 25, 26, 57, 63, 73, 78, 79, 80, 127, 128 Rubenstein, R., 25, 28 Author Index S S´ nchez, V., 25, 26, a Samantha, J., 178 Santos, L., 205 Santos, S C., 205 Sayac, N., 35, 49, 50, 53, 93, 98 Schon, D., 121 Schauble, L., 146 Schwille, J., 93 Seago, N., 211, 216, 219, 220 Serrazina, L., 201, 202 Sfard, A., 26, 42, 145, 168, 169, 174 Shavelson, R J., 164 Shealy, B., 213 Sherin, M G., 213 Shimizu, Y., 176 Shulman, L., 19, 25, 106 Shulman, L S., 212, 213, 214 Sierpinska, A., 150, 186 Silver, E A., 9, 185, 195, 245, 246 Simmt, E., 26, 151, 152, 153, 155, 158, 159, 160, 161, 163, 165 Simon, M., 213 Sinkinson, A., 117 Skott, J., 27, 57, 66, 99 Skovsmose, O., 42 Sleep, L., 95 Smith, A., 113 Smith, M S., 186, 191 Snyder, W., 174 Sowder, J T., 180 Squalli, H., 217 Stacey, K., 130 Stainton, R., 114 Steffe, L P., 150 Stein, M K., 186, 245, 246 Stevenson, H., 95, 97 Stigler J W., 176, 177, 187 Stigler, J., 95, 97, 99, 147, 258 Stiles, K E., 168 Sullivan, P., 48, 53, 186, 187, 213 Sumara, D., 158 Swafford, J., 145, 186, 212 T Tabachnik, B., 83 Taplin, M., 123, 124 Tatto, M T., 13, 15, 16 Tatto, T., 93, 135 Tenoch Cedillo, 149 Terry Wood., 8, 143, 211 Thames, M., 95, 127, 129 Thompson, A., 83 Author Index Thompson, A G., 213 Thwaites, A., 25, 57, 63, 73, 78, 80, 128 Tirosh, D., 13, 15, 57, 61 Towne, L., 164 Tsamir, P., 57, 61 Tsui, A B M., 146 Tzur, R., 105, 108, 140 V Vale, I., 128, 188, 219, 250 Valsiner, J., 62, 88 van den Heuvel-Panhuizen, M., 8, 144, 185, 199, 200, 202 van Es, E A., 213 van Maanen, J., 212 Varandas, J M., 46 Varela, F., 218 Verschaffel, L., 27 Viadero, D., 115 Villarreal, M E., 202 Vygotsky, L., 62, 88, 106, 228 W Walen S B., 189 Wallach, T., 59 Walshaw, M., 59 Wearne, D., 186 269 Wenger, E., 26, 145, 151, 170, 171, 172, 173, 174, 175 Wertsch, J V., 26 White, A., 93, 95 Whitehead, J., 114 Whiting, C., 114 Whitty, G., 114 Wiggins, G., 178 Wiliam, D., 131 Williams S R., 189 Wilson, M., 216 Winsløw, C., 25, 57, 58, 71, 73, 93, 136 Wollring, B., 35, 42, 43, 44 Wood, T., 8, 93, 97, 143, 144, 146, 211, 216 Y Yoshida, M., 176 Z Zanette, L., 35, 45, 66, 202 Zaslavsky, O., 103, 105, 106, 107, 108, 109, 137, 139, 140, 185, 186, 187, 188, 189, 190 Zazkis, R., 26, 30 Zeichner, K., 83 Zodik, I., 108, 109 Zulatto, R B A., 205 Subject Index Note: The letters ‘f’ and ‘t’ following the locators refer to figures and tables respectively A Academic mathematics, 35–36, 39, 75, 94–95 Action knowledge, concepts of, 85 Adaptive/learning systems (Davis & Simmt), 155 Analysing professional practices, 49 Association of Mathematics Education Teachers, 113 Association of Teachers of Mathematics, 113 Attitudes/beliefs “in theory” and practice enacted/espoused beliefs, 77 See also Student teachers voices/beliefs and attitudes, study of Avoidance adaptations, 64, 84 B Baby boomers, 117 Basic-level categories, 160 “Behind-the-screen” approach, 156 Beliefs/attitudes, in theory and practice enacted/espoused beliefs, 77 See also Student teachers voices/beliefs and attitudes, study of “Bodies,” 150 British Society for Research into the Learning of Mathematics, 113 “Burning-Animator,” 156 CBMS, see Conference Board on Mathematical Sciences (CBMS) C “Centred stance of teaching practitioners,” 48, 49, 65 Cheme for the pre-service teachers’ activities (Sayac), 49–50 Classrooms interaction, collaborative interpretation of, 51, 65 systematic observations, 78–79 See also Student teachers voices/beliefs and attitudes, study of COACTIV (Cognitive Activation in the Classroom: Learning Opportunities for the Enhancement of Mindful Mathematics Learning), 214 Cognitive Activation in the Classroom: Learning Opportunities for the Enhancement of Mindful Mathematics Learning (COACTIV), 214 Collective participation (Siemon), 155 Collective product, 174 Community of interpretation, 65 Concurrent preparation, definition, 18 Conference Board on Mathematical Sciences (CBMS), 127 “Constructivist teaching,” 252 Content and Language Integrated Learning approach, 67 Content knowledge and pedagogy, relationship COACTIV, 214 factors affecting teacher flexibility, 213 PCK, facets of, 214–215 PISA, 214 “powerful parents,” 215 social/institutional factors of teaching, 215–216 Continuing professional development (CPD), 113, 115, 116 Co-observation and co-teaching, 165 271 272 CPD, see Continuing professional development (CPD) “Critical Issues in Mathematics Education,” workshop, 127 D “De-centred stance of observers,” 49, 65 “Decompressing” (unpacking), mathematical ideas, 220 Didactical knowledge, 25, 26, 29, 30, 57, 60, 62 E Educational Studies in Mathematics, 161, 249 Education of future mathematics teachers, purposes for, 35 Educators, reflection on practice, 121–122 pre-service teachers, learning of mathematical or pedagogical problem solving, 124 specific mathematics concepts, 123–124 as reflective practitioners, 121–122 research, sample studies, 122–123, 123t as researchers, 122 Educators and teacher training context content/pedagogy course survey, 131–133 mathematicians in pedagogy, actual/desired role of, 131–133 mathematics educators in content courses, actual/desired role of, 131 mathematical habit of mind, 128–130 “Math Wars,” 127 mutual interest, ideas of, 127–128 MHM, 128–130 plausible reasoning, 129 “Egalitarian dialogue” (Bairral & Gim´ nez), e 155 Elementary teachers education programmes, 28 and mathematics, 27 Emotional intelligences, 242 Experienced teachers (mentors), 60 F Fostering Algebraic Thinking Toolkit (AT), 220 G “Golden Hellos,” 114 “Grid game,” 40–41, 41f, 42f I ICME, see International Congress on Mathematical Education (ICME) Subject Index ICMI, see International Commission on Mathematical Instruction (ICMI) 15th ICMI Study, the Professional Education and Development of Teachers of Mathematics, ICMI study on professional education and development of teachers of mathematics, setting stage for design of study, 6–7 scope and focus, 3–6, 4t study on professional education of mathematics teachers, 2–3 study volume, 7–9 ICT, see Information and communications technology (ICT) “ICT culture,” 46 ICT-rich mathematical-education environment, 46 Inductive reasoning, see Plausible reasoning Information and communications technology (ICT), 45, 116 Initial mathematics teacher education (ITE) comments and reflections, 135–138, 139–140, 227–230 curriculum of teacher preparation, 11 early years of teaching, 12 history/change in teacher preparation, 12 nature of diversity, 11 problems of preparing teachers, 12 recruitment and retention, 11 structure of teacher preparation, 11 Initial teacher education (ITE), 113 Initial teacher training (ITT), 14, 113, 130 “Inquiry communities,” 155 Institutional transition, 96–98 See also Teaching, early years Institut Universitaires de Formation des Maˆtres (IUFM), 49 ı Interaction in everyday mathematics classes steady flow vs thickened interaction, 51 International Commission on Mathematical Instruction (ICMI), International Congress on Mathematical Education (ICME), 249 10th International Congress on Mathematics Education (ICME 10), 2, 249–250 Internet environment, 205 Interpreting students’ voices engage in solving mathematics problems, 74 questionnaires and interviews, 74 See also Student teachers voices/beliefs and attitudes, study of Subject Index Isolated teacher practice, phenomenon of, 98 ITE, see Initial teacher education (ITE) ITT, see Initial teacher training (ITT) IUFM, see Institut Universitaires de Formation des Maˆtres (IUFM) ı J JMTE, see Journal of Mathematics Teacher Education (JMTE) Journal for Research in Mathematics Education (JRME), 249 Journal of Mathematics Teacher Education (JMTE), 2, 118, 249, 251–252 under-researched topic, 180 JRME, see Journal for Research in Mathematics Education (JRME) Jugyou kenkyuu (Japanese lesson study), 176 K “Knowledge-in-action,” 63 Knowledge Quartet, 26, 63, 78, 104, 127–128 L Lacanian psychoanalytic theory, 154 Learning and professional development, models on four areas, teacher-interns, 177–178 lesson study, nonlinear/overlapping phases, 176–178 professional development materials, 178–179 toolkit of Star Schools project, 178–179 theory in practice, reflecting on classroom communication and discourse, 179 Learning and Teaching Linear Functions: Video Cases for Mathematics Professional Development (LF), 220 Learning and Teaching Linear Functions (LTLF), 219, 220 Learning communities, 196–202 issues in, 197–201 learning through collaboration from professionals, 198 multi-approach experience-based learning, to be coordinator, 200 notion of, 197 stories of practice, tool in pre-service secondary mathematics teacher education, 199 understanding/transforming practice, Portuguese experience, 201–202 Learning in and from practice, 8, 143 background, 143–144 chapters (four), 144–145 273 learners in and from practice, 145–147 personal response, 231–236, 235t Learning through teaching (LTT), 216 LTLF, see Learning and Teaching Linear Functions (LTLF) LTT, see Learning through teaching (LTT) M Mathematical Association, 113 Mathematical habit of mind (MHM), 128 descriptions of, 129 Mathematical Sciences Research Institute, California, 127 “Critical Issues in Mathematics Education,” workshop, 127 Mathematics and pedagogy, balance of teacher knowledge domains of teacher knowledge content knowledge and pedagogy, see Content knowledge and pedagogy, relationship implications for practicing mathematics teachers’ development, 220–221 learning from practice, 216–220 impact of LTLF materials on teachers, 219 interpretation of logic of pupils, 218 interpretation of pupils’ productions, 219 kinds of teaching strategies appear, 219 learning through teaching (LTT), 216 LTLF, 219 Piagetian disequilibration, 217 sensibilities of teachers, 219 Mathematics educators (didacticians), 60 Mathematics educators’ knowledge and development models, 105–108 reflective practice, 105 Steinbring’s model, modification of, 107t Teaching Triad (Jaworski’s), modification, 106–107, 107t task stemming from teacher educator’s research, example of, 108–110 rhombus problem, the, 108–110, 109f Mathematics teacher training, components of, 31f knowledge and beliefs, 25–27 research in initial education, past/present/future, 29–30 structures of initial teacher education, 27–29 274 Matheracy, 243 Math for Future Primary Teachers, University of Kentucky, 129 “Math Wars,” 127 “Metacommenting,” 156 MHM, see Mathematical habit of mind (MHM) Models on learning and professional development four areas, teacher-interns, 177–178 lesson study, nonlinear/overlapping phases, 176–178 professional development materials toolkit of Star Schools project, 178–179 theory in practice, reflecting on classroom communication and discourse, 179 Mode/median/average, mathematical task, 44–45 “Multi-logue,” 179 Multiple intelligences, 242 Multiplication of two-digit numbers, activities for, 38 N Non-verbal instructions, 43f–44f Non-verbal language, development and use of, 43 Normative adaptations, 84 O “Open provocateur,” 156 P PBPD, see Practice-based professional development (PBPD) PCK, see Pedagogical content knowledge (PCK) “Pedagogical content knowledge,” 19 Pedagogical content knowledge (PCK), 25, 78 Pedagogical knowledge (PK), 25 Pedagogy, emphasis on, 19 “Perfect teachers,” 35 Personal transition, 98–99 See also Teaching, early years PGCE, see Post-Graduate Certificate in Education (PGCE) Piagetian disequilibration, 217 PISA, see Programme for International Student Assessment study (PISA) PK, see Pedagogical knowledge (PK) Plausible reasoning, 128, 129 Post-Graduate Certificate in Education (PGCE), 117 Powerful tasks, 187 activities based on student work, 189–190 Subject Index considering alternative definitions of square, 188 from use of instructional example to task, 190 Practice-based model of professional development, 169 Practice-based professional development (PBPD) features of, 246 professional learning tasks, role of, 245t Practice-based theory of mathematical knowledge for teaching, 95 Practicum, integrated part of teacher education programme and issues of national/cultural differences, 65–67 practicum, definition, 58 specific ways of using practicum, 63–65 structural ways of using practicum, 60–61 “learning-in-action rather than learning-about-action,” 60 teacher education programmes at tertiary educational institutions disciplinary studies/educational studies/teaching practice, 57 theoretical tools to use practicum, 61–63 Practising mathematics teacher education activating understanding of school mathematics, 36–42 enhancing communication of mathematical ideas, 42–45 limitation, 53–54 social positions with respect to classroom practice, 49t studying classroom practice, 48–53 interaction, mathematics classes, 51 pre-service teachers, as teacher educators, 50–51 re-centring, 48–50, 52, 65 Sayac, scheme for pre-service teachers activities, 49–50 social positions with respect to classroom practice, 49t using information and communication technology, 45–48 basic support for cooperative work, 47 ICT-rich environments, 46 Preparation of teachers, 11–12, 13–14 Pre-service teachers definition, 28 education, 18, 64, 71, 73, 75, 79, 83–90, 93, 158, 197 Subject Index learning, categories, 122 learning of mathematical or pedagogical problem solving, 124 specific mathematics concepts, 123–124 views of the teacher education program (Bednarz & Proulx), 85t Problem solving, books on (Polya), 130 Professional development directions for further research, 179–182 on learning and communities of practice, 174–175 as participation in social practices, 173–174 practice and learning, dimensions, 171–173 on learning and professional development, 175–176 models, see Models on learning and professional development practice-based model, 169 programs, 116 questions, relevant, 181 training model, 167–169 from training to practice-based professional development, 169–170 Professional learning for and in practice, strand ii, 5–6 “Professional learning units,” 116 Programme for International Student Assessment study (PISA), 214 Projective adaptations, 84 Prospective teachers, 5, 12, 20, 28, 29, 108, 129, 158, 257 Pseudo-theoretical appellations, 252 Psychology of Mathematics Education (PME), 2, 204, 249 Public writing in field of mathematics teacher education defining scope/nature of field, ICME 10 survey, 249–250 claims, 250 JMTE, pseudo-theoretical appellations, 252 research programmes mathematics for teaching, 252–253 research partnerships between teachers and educators, 253–254 Pugwash Manifesto (1955), 242 Q QUANTUM research project, 253 275 R “Re-centring stance of legitimate selfregulation of community of interpretation,” 65 Reflections on education/ mathematics/mathematics education goals of education, 239–240 establishing educational systems, purpose, 239 mathematics and mathematics education in a changing civilization, 242–244 role of mathematics education, 240–241 teaching mathematics, reason, 241–242 Reflective practice, 105 Reification, 173 Rhombus problem, the, 108–110 S “Salary scale,” 115 School experience during pre-service teacher education, students’ perspective (dis)connections with university coursework, 83–86 redefinition of “objective,” 86 type of adaptations, factors, 84 learning from experience, school contexts/personal histories/university coursework, 88–89 vignettes from case study of transition from pre-service to beginning teaching, 89t personal histories and embedded traditions, 86–87 relation to mathematics, 86 pre-service teacher views of teacher education program (Bednarz & Proulx), 85t School mathematics ICT-rich school mathematics, 48 “traditional,” 35–42 SMK, see Subject-matter knowledge (SMK) Special education, 116 Spiritual intelligence, 242, 243 Star Schools project, toolkit of, 178–179 “Static deficiency,” 160 Steinbring’s model, modification of, 107t “Structuring resources” concepts of, 85 Student teachers, strategy to activate, 37–40 Student teachers voices/beliefs and attitudes, study of characterization of teachers (Proulx, 2005), 76t–77t 276 Student teachers voices/beliefs and attitudes, (cont.) interpreting students’ voices, 74–77 engage in solving mathematics problems, 74 questionnaires and interviews, 74 responses of students, 76 issues of methodology, 73–74 relations between attitudes and beliefs “in theory” and practice, 77–78 systematic observations of classrooms, 78–79 tensions and challenges for teacher education, 79–80 Subject Knowledge in Mathematics (project), 128 Subject-matter knowledge (SMK), 25, 63, 78, 216 “Supporter,” 156 “Sustained conversations” (Dawson), 155 T Teacher interns, four areas, 177–178 knowledge, strands content/pedagogical/didactical knowledge, 25 “Teacher developers,” 257–258 Teacher education in England, 114 reason, 29 systems, components, 15 systems across world directions/questions for future research, 20–21 institutional characteristics, 17–18 structure and approaches to teacher education, 18–19 emphasis on mathematics content/pedagogy, 19 practicum experiences, 20 system characteristics, 16–17 Teacher educator, becoming national programme of support, 116–118 baby boomers, 117 ITE tutor, role of, 117 PGCE, 117 Post-Graduate Certificate in Education (PGCE), 117 role of, 115–116 perspectives from united kingdom and US teacher educator, route to becoming, 114–115 Subject Index Teacher preparation programs and early years of teaching, (strand i) curriculum of teacher preparation, early years of teaching, history and change in teacher preparation, most pressing problems of preparing teachers, 4–5 recruitment and retention, structure of teacher preparation, “Teachers’ backgrounds,” 153 Teacher’s learning in virtual communities, 202–206 Teachers of mathematics, practice and research on professional education/development of need to focus teachers’ education on practice, 255–259 teacher developers, identification and development of, 256–257 valid and reliable assessments of teachers’ learning, 257–258 Teachers’ professional knowledge, didactical/pedagogical/curricular/pedagogical content knowledge, 75 Teacher Training Agency (TTA), 113 Teacher Training Resource Bank, 113 Teaching, early years epistemological transition, 94–96 academic/school mathematics, divide between, 94 collaborative “lesson study,” 95 “practice-based theory of mathematical knowledge for teaching,” 95 ‘punctual level,’ 94 institutional transition, 96–98 personal transition, 98–99 isolated teacher practice, phenomenon of, 99 Teaching in and from practice, development of benchmarks, recognized enacted beliefs, 159–161 explicit beliefs, 157–159 teacher attitudes, 161 factors, recognized structures for intervention, 155–156 teacher positioning, 153–155 teachers’ backgrounds, 152–153 teachers’ epistemological frames, 150–152 issues, recognized contextual and situational matters, 163–164 embracing complexity, 164 Subject Index making and unmaking distinctions, 162–163 overview, 149 Teaching Triad (Jaworski), 106–107, 186 modification of, 107t “Team player,” 156 Technology in education, 116 Technoracy, 243 Tools and settings supporting, learning in and from practice communities, learning, see Learning communities features of tasks for mathematics teacher education, 186–190 See also Powerful tasks instructional episodes, 191–196 changes, ways of coping with problematic learning situations in geometry instruction, 192–193 lesson study, successful use of, 196 problematic learning situation, perpendicular lines, 194–195 video and narrative cases, 192 teacher’s learning in virtual communities, 202–206 dialogic use of teleinteractions for distance geometry teacher training (12–16 years old) as equity framework, 203 277 internet access, 202–206 internet-based continuing education programs, 204 video conferences/chat rooms, 205 Training model of professional development, 167–169 Training to practice-based professional development, 169–170 TTA, see Teacher Training Agency (TTA) U “Using and Applying Mathematics,” 130 V “Vibrant sufficiency,” see Teaching in and from practice, development of Video-recording lessons, 74 “Virtual world,” 205 W Withdrawal adaptations, 84 Z Zone of Free Movement (ZFM), 62, 88, 139 Zone of Promoted Action (ZPA), 62, 88 Zone of Proximal Development (ZPD), 62, 88, 139, 228 NEW ICMI STUDY SERIES M Niss (ed.), Cases of Assessment in Mathematics Education An ICMI Study 1992 (The 6th ICMI Study) M Niss (ed.), Investigations into Assessment in Mathematics Education An ICMI Study 1992 (The 6th ICMI Study) G Hanna (ed.), Towards Gender Equity in Mathematics Education An ICMI Study 1996 (The 7th ICMI Study) A Sierpinska and J Kilpatrick (eds.), Mathematics Education as a Research Domain: A Search for Identity An ICMI Study 1998 (The 8th ICMI Study) C Mammana and V Villani (eds.), Perspectives on the Teaching of Geometry for the 21st Century An ICMI Study 1998 (The 9th ICMI Study) J Fauvel and J van Maanen (eds.), History in Mathematics Education The ICMI Study 2000 (The 10th ICMI Study) D Holton (ed.), The Teaching and Learning of Mathematics at University Level An ICMI Study 2001 (The 11th ICMI Study) K Stacey, H Chick and M Kendal (eds.), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study 2004 F.K.S Leung, K.-D Graf and F.J Lopez-Real (eds.), Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West: The 13th ICMI Study 2006 10 W Blum, P L Galbraith, H.-W Henn, and M Niss (eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study 2007 11 R Even and D Loewenberg Ball (eds.), The Professional Education and Development of Teachers of Mathematics: The 15th ICMI Study 2009 0-7923-2089-1 HB 0-7923-2095-6 HB 0-7923-3921-5 HB 0-7923-3922-3 PB 0-7923-4599-1 HB 0-7923-4600-9 PB 0-7923-4990-3 HB 0-7923-4991-1 PB 0-7923-6399-X HB 1-4020-0942-9 PB 0-7923-7191-7 HB 1-4020-0072-3 PB 1-4020-8130-8 HB 0-387-29722-7 HB 0-387-29820-7 HB 978-0-387-09600-1 HB Information on the ICMI Study program and on the resulting publications, including Studies to 5, can be obtained at www.mathunion.org/ICMI/ or by contacting the ICMI SecretaryGeneral, whose email address is available on the ICMI website ... in the Faculty of Education in the University of Western Ontario Paper presented at the conference of the 15th ICMI Study on ´ the Professional Education and Development of Teachers of Mathematics, ... programmes and early years of mathematics teaching in Uganda Paper presented at the conference of the 15th ICMI Study on the Professional ´ Education and Development of Teachers of Mathematics, ... programmes and early years of mathematics teaching in Uganda Paper presented at the conference of the 15th ICMI study on the Professional ´ Education and Development of Teachers of Mathematics,